arXiv subjects

Christian Parkinson

Publications and source records attributed to Christian Parkinson.

20 records · Page 2Linked to original sources

arXiv2018

Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach

We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal walking path by solving an ordinary differential equation. We demonstrate the effectiveness of our method by computing optimal paths which travel throughout mountainous regions of Yosemite National Park. We include details regarding the numerical implementation of our model and address a specific application of a law enforcement agency patrolling a nationally protected area.

math.OC↗

arXiv2015

Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity

We consider a spatially-heterogeneous generalization of a well-established model for the dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The model consists of a nonlinear system of three coupled reaction-diffusion equations with parameters that may vary spatially. Upon formulating the model, we prove that it preserves the positivity of initial data and construct global-in-time solutions that are both bounded and smooth. Finally, additional results concerning the local and global asymptotic behavior of these solutions are also provided.

math.AP↗